Normal form in Hecke-Kiselman monoids associated with simple oriented graphs
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Published:2020
Issue:2
Volume:30
Page:161-171
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ISSN:1726-3255
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Container-title:Algebra and Discrete Mathematics
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language:
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Short-container-title:ADM
Author:
Aragona R., ,D'Andrea A.,
Abstract
We generalize Kudryavtseva and Mazorchuk's concept of a canonical form of elements [9] in Kiselman's semigroups to the setting of a Hecke-Kiselman monoid HKΓ associated with a simple oriented graph Γ. We use confluence properties from [7] to associate with each element in HKΓ a normal form; normal forms are not unique, and we show that they can be obtained from each other by a sequence of elementary commutations. We finally describe a general procedure to recover a (unique) lexicographically minimal normal form.
Publisher
State University Luhansk Taras Shevchenko National University
Subject
Discrete Mathematics and Combinatorics,Algebra and Number Theory